Question

Find a unit vector in the direction of $\overrightarrow{a}=2\hat{i}-3\hat{j}+6\hat{k}$.

Answer 1

Given:
$$\begin{gathered} \overrightarrow{a}=2\hat{i}-3\hat{j}+6\hat{k} \\ \left|\overrightarrow{a}\right|=\sqrt{2^2+{\left(-3\right)}^2+6^2}=\sqrt{4+9+36}=\sqrt{49}=7 \end{gathered}$$
Unit vector = $\frac{\overrightarrow{a}}{\left|\overrightarrow{a}\right|}=\frac{2\hat{i}-3\hat{j}+6\hat{k}}{7}=\frac{2}{7}\hat{i}-\frac{3}{7}\hat{j}+\frac{6}{7}\hat{k}$